How to recognize with just name and last name if the person is a political exposed person
But if they enter a name that is not in any of their data sources, how would I train a model to decide if its pep or not?


Based on just a person's name and nothing else, the accuracy of this model is going to be very low. Consider that most first name, surname combinations in Europe are going to be repeated across the population.

However, the accuracy might still be slightly better than guessing. Some families and social classes could be more likely to be involved in political work, and a statistical model would pick up on that.

To train the model, take your positive names, and combine with a random selection of names of people that are known to be "not political" or similar enough. It doesn't matter if some of the names are the same provided you are confident in your data. Probably you could just take a phone directory or the electoral register or some other list of general names. Provided your "political" people are a small fraction of all people, this will work well enough even if you have some of them in the negative class.

Ideally you mix those name groups in the rough proportion that the bank expects to see "political" and "non-political" customers, so that your data set is a good representation of the target population.

Then you train a classifier on the names. As this is text and sequence data, you will need a solution for that. Possibly LSTM would be suitable architecture, but so might some feature selection from the names in a more simple ML model.

Remember to hold back some data (both positive and negative cases) for cross-validating and testing the model.

Expect the accuracy of your model when testing to be low. Very low. I would not at all be surprised to find the end result unusable by itself.

If this is seriously to be part of some bank's account setup process, there needs to be additional data used later in the process. A gate for additional checks based purely on someone's name will perform very poorly in my opinion.